The <Friedmann acceleration equation> and $H=\dot a/a$ give the <deceleration parameter>
$$
q=-\frac{\ddot a}{aH^2}
=\frac{4\pi G}{3H^2}\sum_i\rho_i(1+3w_i)
=\boxed{\frac12\sum_i\Omega_i(z)(1+3w_i)}.
$$
An <Einstein-de Sitter universe> contains only <pressureless matter>, so $q_0=1/2$ and cannot explain the observed negative value. For the stated <Lambda-CDM model>,
$$
q_0=\frac12\left[0.3+0.7(1-3)\right]=-0.55,
$$
so its <cosmological constant> produces the required <accelerating universe>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 310 / 1 / b / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-310/1/b/solution